PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Preservice Secondary Teachers’ Understanding of the Cartesian Connection and Equivalence
Page: 916
Both prior research and national standards emphasize the importance of critical ideas, such as the Cartesian Connection and equivalence, in algebra problem solving. The mathematics education community, however, has yet to determine whether the secondary teachers who teach such ideas fully grasp these ideas themselves. To investigate this, I interviewed a cohort of nine preservice secondary teachers in a teacher education program with two algebra problems that embed these ideas. The results showed that many of the teachers failed to understand equivalence as a relation between geometric objects, and thus could not solve an algebra problem by relating algebraic equations to their corresponding graphs. Many also misinterpreted the meaning of the term “solution,” and thus could not use the Cartesian Connection to find a solution of an equation. It is advisable that secondary teacher education programs focus more on these critical ideas so that secondary teachers can impart such ideas on their students.